How can you copy a weight paint from a Bone in one object to a bone in another object
Yes it is, even if the two objects are not identical.

Move the two objects in the same spot, select the destination object (or objects), THEN shift select the source, then press F3 (search operator) and type "data", choose the "Transfer mesh data" operator, choose "vertex groups". If the objects are the same all others default options should be OK.

After generating the copied vertex groups, you can rename them accordingly with the names of the new deforming bones